NDA Math Heights and Distance

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Consider the following for the next three (03) items that follow :
ABC is a triangular plot with AB=16m, BC=10m and CA=10m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45∘ at the vertex B.

[NDA II 2022]

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What is the height of the lamp post ?

[NDA II 2022]

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